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A block coordinate variable metric linesearch based proximal gradient method

Author

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  • S. Bonettini

    (Università di Modena e Reggio Emilia)

  • M. Prato

    (Università di Modena e Reggio Emilia)

  • S. Rebegoldi

    (Università di Ferrara)

Abstract

In this paper we propose an alternating block version of a variable metric linesearch proximal gradient method. This algorithm addresses problems where the objective function is the sum of a smooth term, whose variables may be coupled, plus a separable part given by the sum of two or more convex, possibly nonsmooth functions, each depending on a single block of variables. Our approach is characterized by the possibility of performing several proximal gradient steps for updating every block of variables and by the Armijo backtracking linesearch for adaptively computing the steplength parameter. Under the assumption that the objective function satisfies the Kurdyka-Łojasiewicz property at each point of its domain and the gradient of the smooth part is locally Lipschitz continuous, we prove the convergence of the iterates sequence generated by the method. Numerical experience on an image blind deconvolution problem show the improvements obtained by adopting a variable number of inner block iterations combined with a variable metric in the computation of the proximal operator.

Suggested Citation

  • S. Bonettini & M. Prato & S. Rebegoldi, 2018. "A block coordinate variable metric linesearch based proximal gradient method," Computational Optimization and Applications, Springer, vol. 71(1), pages 5-52, September.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-018-0011-5
    DOI: 10.1007/s10589-018-0011-5
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    Cited by:

    1. Bonettini, S. & Prato, M. & Rebegoldi, S., 2021. "New convergence results for the inexact variable metric forward–backward method," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Silvia Bonettini & Peter Ochs & Marco Prato & Simone Rebegoldi, 2023. "An abstract convergence framework with application to inertial inexact forward–backward methods," Computational Optimization and Applications, Springer, vol. 84(2), pages 319-362, March.
    3. Valeria Ruggiero & Gerardo Toraldo, 2018. "Introduction to the special issue for SIMAI 2016," Computational Optimization and Applications, Springer, vol. 71(1), pages 1-3, September.

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